Problem: Divide the polynomials.
Explanation: Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{4x^3-3x+1}{x}=\dfrac{4x^3}{x}-\dfrac{3x}{x}+\dfrac{1}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{4x^3}{x}&=4x^2 \\\\ -\dfrac{3x}{x}&=-3 \end{aligned}$ $\dfrac{1}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $4x^2-3+\dfrac{1}{x}$ [I want to see a different way of performing the division.]